First difference,
[tex]\Delta_{1} = a_{2} - a_{1} = 3 - 1 = 2 = 1 + 1[/tex]
Second difference,
[tex]\Delta_{2} = a_{3} - a_{2} = 6 - 3 = 3 = 2 + 1[/tex]
Third difference,
[tex]\Delta_{3} = a_{4} - a_{3} = 10 - 6 = 4 = 3 + 1[/tex]
And so on.
Assuming the pattern holds on, we see that
i-th difference,
[tex]\Delta_{i} = a_{i + 1} - a_{i} = i + 1[/tex]
[tex]\implies a_{i + 1} = a_{i} + i + 1[/tex]
Then, nth term is,
[tex]\implies a_{n} = a_{n - 1} + n[/tex]
[tex]= a_{n - 2}+ (n + (n - 1))[/tex]
[tex]= a_{n - 3} + (n + (n - 1) +(n - 2))[/tex]
[tex]= a_{n - (n - 1)} + \sum \limits^{n - 2}_{k = 0}(n - k)[/tex]
[tex]= a_1 + \sum \limits^{n - 2}_{k = 0}n- \sum \limits^{n - 2}_{k = 0}k[/tex]
[tex]= a_1 +n(n -2 + 1 )- \frac{1}{2} (n - 2)(n - 1)[/tex]
[tex]= a_1 +n(n -1 )- \frac{1}{2} (n - 2)(n - 1)[/tex]
[tex]= a_1 +(n -1 )(n- \frac{1}{2} (n - 2))[/tex]
[tex]= a_1 + \frac{1}{2} (n -1 )(2n- n + 2)[/tex]
[tex]= a_1 + \frac{1}{2} (n -1 )(n + 2)[/tex]
[tex]\implies a_{n} = 1 + \frac{1}{2} (n -1 )(n + 2)[/tex]
Now, the 21st term in the sequence is,
[tex]\implies a_{21} = 1 + \frac{1}{2} (21 -1 )(21 + 2)[/tex]
[tex]= 1 + \frac{1}{2} \times 20 \times 23[/tex]
[tex]= 231[/tex]
plz help...........
Answer:
1 is one of them
Step-by-step explanation:
$36 - $12.75 =
Pls answer
Jesus is looking for a new gym Fitness Connection costs $6 to join with a monthly fee of $14. Fitness World costs $10 to join with a monthly of \$12 . Which oquation and solution represent the number of months will take for both gymo to cost the same?
jesus do be gettin buff doe
Answer the link at the bottom plz
Answer:
2/3
Step-by-step explanation:
24students - 8 boys = 16 girls
16/24
2/3
Answer:
[tex]\frac{16}{24}=\frac{2}{3}[/tex]
also
[tex]\frac{8}{24} =\frac{1}{3}[/tex]
Step-by-step explanation:
Write a multiplication fact that goes with this division fact.
33 ÷ 11 = 3
Answer: 3 x 11 = 33
Step-by-step explanation: Hope it helped!
what is the simplest form of this ratio?
100:40:20
Answer:
52
Step-by-step explanation:
y=x-1
y=x+1
((This is System of Equations))
Add 1 to both sides of the equation.
y = x - 1
2x = 3 + 1
Add 3 and 1 .
y = x - 1
2x = 4
The variables x an y vary directly. When x=13, y=52. Which equation correctly relates x and y?
Answer:
The equation which correctly relates x and y is y = 4x
Step-by-step explanation:
The equation of the direct variation is y = k x, where
k is the constant of variationTo find the value of k, use the initial values of x and y∵ The variables x and y vary directly
→ Use the form of the equation above
∴ y = k x
∵ When x = 13, y = 52
→ That means the initial values of x and y are 13 and 52
∴ x = 13 and y = 52
→ Substitute them in the equation above to find k
∵ 52 = k (13)
∴ 52 = 13k
→ Divide both sides by 13
∴ 4 = k
∴ The value of k is 4
→ Substitute it in the equation
∴ y = 4x
∴ The equation which correctly relates x and y is y = 4x
Question 2 of 10
Is ABC - ALMN? If so, name which similarity postulate or theorem applies.
B
75°
75
50"
А
50"
C
N
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
A
Step-by-step explanation:
two of the triangles' corresponding angles are the same even if the side lebgths are not, making these two similar
By AA similarity triangle ABC and triangle LMN are similar. Therefore, option A is the correct answer.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
In the given triangle ABC, ∠A=50° and ∠B=75°.
In the given triangle LMN, ∠L=50° and ∠M=75°
From the given triangles,
∠A=∠L=50°
∠B=∠M=75°
By AA similarity triangle ABC and triangle LMN are similar.
Therefore, option A is the correct answer.
To learn more about the similar triangles visit:
https://brainly.com/question/25882965.
#SPJ5
Find the value of Angle A and B!!! Will mark brainliest
Answer:
A=73
B=107
Step-by-step explanation:
since the angles are across from eachother they would be the same, the total angle of all 4 added together would be 360, and 73+107 would be 180, so 180+180 is equal to 360
The function y - 3 = 4(x + 2) is in point-slope form. Select the equivalent equation in slope-intercept form
y = 112 +4
y = 4.3 +11
y = 4x + 5
y = 4x + 8
7x – 2y = -5 which is the correct answer help a homie out pls
Suppose Metro by T-Mobile wants to offer a simple extended warranty plan. If your phone is damaged, they will repair it for up to $50. If you lose or destroy your phone, they will give you a $200 voucher towards a new phone. The company believes that 5% of customers will need the replacement voucher and 10% will request a repair. What is the standard deviation?
Answer:
45
Step-by-step explanation:
Given that :
Voucher awarded (x) :
Repair = $50
Lose or destroy = $200
P(x):
Replacement voucher = 5%
Repair voucher = 10%
X ______ 50 ______ 200
P(x) ____ 0.1 _______ 0.05
Expected variance Var(X) :
ΣX²p(x) - E(x) ;
E(x) = Σx*p(x) = (50*0.1) + (200*0.05) = 15
ΣX²p(x) = Σ[(50^2 * 0. 1) + (200^2 * 0.05)] = 250 + 2000 = 2250
Var(X) = 2250 - 15^2 = 2025
Standard deviation = √Var(x)
Standard deviation = √2025
Standard deviation = $45
Find the value of 3w-1 given that - 2w+8= 6.
Simplify your answer as much as possible.
Answer:
-4
Step-by-step explanation:
Given 2w + 8 = 6, find w
2w = -2w = -1found w = -1, sub it into 3w - 1
3w - 1 = 3(-1) -1-3 - 1= -4Which equation could be used to find the value of x in the triangle below? (pls help)
Answer:
B.
Step-by-step explanation:
All of it needs to add up to 180
So you have
2x + 4x+10 + 6x-10 = 180
Combine like terms
12x=180
what is the answer?
Answer:
HL
Step-by-step explanation:
The hypotenuse and the "leg" are congruent...along with the 90 degree angle.
"The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent." - Calcworkshop
What is the Slope of the line?
Answer:
1/2
Step-by-step explanation:
●••□■♤□●|□¤○|€♡■●~3}£₩9¥¥♡♡■{{6899
I need help finding a, b, and c. Thank you!
the radius of the base of a right cylinder is 12 cm and the height and the height of the cylinder is 18 cm. in terms of pi what is the volume of the cylinder.
Answer:
Step-by-step explanation:r=12cm,h=18cm,v=?
Vol. Of a cylinder=Πr²h
V= Π×12²×18
V= Π×144×18
V=2592Πcm³
What percent of 35 is 21
Answer:
7.35
Step-by-step explanation:
Answer:
60%
Step-by-step explanation:
Hope this helps!!!
Can I have Brainliest???
Choose the property of real number that justifies the equation. Last time I asked this the picture was cut out! Please answer quick I’m timed!
Answer:
I am thinking it is distributive property
Please help me answer this question thank you !!
Answer:
c
Step-by-step explanation:
3
42 ➗ (15-2)
I don’t know know to do this
Answer:
Step-by-step explanation:
42/13=4
If the ratio of ducklings to mama ducks is 7 to 1 how many ducklings would there be if there were 5 mama ducks? Use a table to solve using ratios!
Help me quickly
Answer:
There would be 35 ducklings
Step-by-step explanation:
If the ratio to baby ducklings to mama ducks is 7 to 1 then the constant of proportionality is 7. So you take the amount of mama ducks and multiply that by 7 you get your answer.
7 x 5 = 35
Put these in order starting from the smallest
62
34
25
59
Answer:
25 34 59 62
Step-by-step explanation:
easy shi thanks
A car lot owner is trying to get rid of this year's inventory to make room for the new vehicles. He paid $25,599 for a red truck. If he sells it to a customer for $22,000, what mark down percentage did he use?
Answer:
14%Step-by-step explanation:
Step one
given data
Cost price of vehicle= $25,599
Selling price of vehicle= $22,000
Required
The percentage discount in the price
Step two:
% discount= cost price-selling price/cost price*100
% discount= 25,599-22,000/25,599*100
% discount= 3599/25,599*100
% discount= 0.140*100
% discount= 14%
The mark down percentage use is 14%
Which relation is a function? Group of answer choices (2, 7), (6, 5), (4, 4), (3, 3), (2, 1) (9, −3), (9, 3), (4, −2), (4, 2), (0, 0) (1, 0), (3, 0), (1, 1), (3, 1) (1, 3) (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
Given:
The relations in the options.
To find:
The relation which is a function.
Solution:
Consider the options are :
(a) {(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)}
(b) {(9, −3), (9, 3), (4, −2), (4, 2), (0, 0)}
(c) {(1, 0), (3, 0), (1, 1), (3, 1) (1, 3)}
(d) {(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)}
A relation is a function if there exist a unique y-value for each x-value.
In option (a), y=7 and y=1 at x=2. So, it is not a function.
In option (b), y=-3 and y=3 at x=9. So, it is not a function.
In option (c), y=0 and y=1 at x=3. So, it is not a function.
In option (d), there are unique y-value for each x-value. So, it is a function.
Therefore, the correct option is (d).
A contestant in a game show has 9,000 points. The contestant answers the next question incorrectly and loses 750 points. Does the word "lose" suggest a positive integer or a negative integer? What integer represents a loss of 750 points?
This question is incomplete
Complete Question
A contestant in a game show has 9,000 points. The contestant answers the next question incorrectly and loses 750 points. Does the word "lose" suggest a positive integer or a negative integer? What integer represents a loss of 750 points?
a) Positive, + 750
b) Positive , - 750
c) Negative , +750
d) Negative , - 750
Answer:
d) Negative , - 750
Step-by-step explanation:
We are told in the question that the contestant has 9000 points
Then he loses 750 points.
This means that the 750 points would be deducted from the 9000 points he the contestant has already.
The word lose is a negative and it carries the Subtraction (-) sign,
hence, lose suggests a negative integer which is given as:
-750
Option d is the correct option
Which expressions are equivalent to (5g+3h+4)•2?
Answer:
nc
Step-by-step explanation:
nc
What is the measure of <6
<6=
Answer:
20/20
Step-by-step explanation: